barking cough is there in infection of larynx and trachea. and you may be right in saying that it may be croup. it can be caused by many of the viruses like RSV, influenza
, para influenza etc.
as you said your daughter is having breathing difficulty, you should take her to emergency immediately to get her checked for her illness and if required she may need a steroid
and nebulization with adrenaline
generally no treatment other than this and paracetamol
is needed to control this ang being self limiting it resolves in few days.
yes there are chances of your four year old of getting this illness. to prevent him you can keep your daughter in isolation until she is free of symptoms.
hope you will be benefited by my answer